mCRE-based parameter identification from full-field measurements: Consistent framework, integrated version, and extension to nonlinear material behaviors

Nguyen, Hai Nam; Chamoin, Ludovic; Minh, Cuong Ha

doi:10.1016/j.cma.2022.115461

Cited by 13 publications

(15 citation statements)

References 60 publications

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“…It is worth noticing in (19) that the parameters are updated following the computation of the gradient in the whole structure and not only where there is a measurement.…”

Section: Stepmentioning

confidence: 99%

“…Numerous researches dealing with mCRE have been conducted, involving forced vibrations dynamics, [13][14][15] transient dynamics 16,17 and nonlinear material behavior. 18,19 Additionally, the mCRE framework has proved its robustness to corrupted 20 and noisy 21 measurements. The classical mCRE approach, as other inversion methods, postulates a constitutive model (even though it is released to inform on possible bias), which has the advantage of being physically interpretable.…”

Section: Introductionmentioning

confidence: 99%

“…It is a flexible compromise between purely data-based approaches [12] which require high data quantity, have high variance and low bias, and model-based approaches which require low data quantity and have low variance and high bias. Numerous researches dealing with mCRE have been conducted, involving forced vibrations dynamics [13,14,15], transient dynamics [16,17] and nonlinear material behavior [18,19]. Additionally, the mCRE framework has proved its robustness to corrupted [20] and noisy [21] measurements.…”

Section: Introductionmentioning

confidence: 99%

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NN‐mCRE: A modified constitutive relation error framework for unsupervised learning of nonlinear state laws with physics‐augmented neural networks

Benady,

Baranger,

Chamoin

2024

Numerical Meth Engineering

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This article proposes a new approach to train physics‐augmented neural networks with observable data to represent mechanical constitutive laws. To train the neural network and learn thermodynamics potentials, the proposed method does not rely on strain‐stress or strain‐free energy pairs but needs only partial strain or displacement measurements inside the structure. The neural network is trained thanks to an unsupervised procedure in which the modified constitutive relation error (mCRE) is minimized. The mCRE functional provides a bias‐aware data assimilation framework with a rich physical sense as the constitutive relation error (CRE) part can be interpreted as a modeling error continuously defined over the structure, and can be used as a prediction quality in the inference phase. This article also extends previous works on the mCRE by introducing a new minimization procedure in the case of nonlinear state laws. As typical structural health monitoring applications may require that the neural networks should be trained online, an important focus is thus made on automatic and adaptive tuning of sensitive hyperparameters (learning rate, weighting between losses, number of epochs and initialization). It is shown that when the training database is rich enough with respect to the loading cases, the proposed method achieves remarkable performance regarding the quality of the learned model, noise robustness, and low sensitivity to user‐defined hyperparameters. The method is evaluated on two test cases: a non‐quadratic potential in the small strain regime with synthetic optic fiber measurements, and a Mooney–Rivlin model in the hyperelastic case with synthetic digital image correlation observations.

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“…It is worth noticing in (19) that the parameters are updated following the computation of the gradient in the whole structure and not only where there is a measurement.…”

Section: Stepmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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NN‐mCRE: A modified constitutive relation error framework for unsupervised learning of nonlinear state laws with physics‐augmented neural networks

Benady,

Baranger,

Chamoin

2024

Numerical Meth Engineering

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“…Although the previously introduced mCRE-based model updating strategy is deterministic, one can show that this procedure is equivalent to the Maximum A Posteriori (MAP) estimation in the Bayesian inference framework with Gaussian distributions, an error norm based on the measurement error covariance matrix, and no a priori on parameters [73,74]. Since covariance on the modeling error is usually not known, the idea is to integrate modeling error in a different manner into Bayesian inference, in a more global and less strict framework that allows more flexibility in the model structure.…”

Section: Interpretation Of the Mcre From A Bayesian Viewpointmentioning

confidence: 99%

Merging experimental design and structural identification around the concept of modified Constitutive Relation Error in low-frequency dynamics for enhanced structural monitoring

Diaz

Charbonnel

Chamoin

2023

Mechanical Systems and Signal Processing

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“…This situation occurs in the in vivo determination of the stress resultants in non-axisymmetric biological membranes [5,18], in the stress monitoring of civil and mechanical shell structures [1] and in bulge (also known as diaphragm or inflation) tests, an experimental procedure used to characterize the biaxial response and identify the material parameters through the inflation of planar membranes or thin shells subjected to a uniform pressure [19][20][21]. In these applications, the stress determination relies on the full-field assessment of the deformed configuration through digital image correlation [22,23].…”

Section: Introductionmentioning

confidence: 99%

Direct stress computations in arbitrarily shaped thin shells and elliptic bulge tests

Suleman

Bosi

2022

Proc. R. Soc. A.

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Most of engineering and biological thin shell structures are characterized by non-axisymmetric and statically indeterminate configurations, which often require the knowledge of the constitutive material model to determine the stress state. In this work, a forward elastostatic method is introduced for the direct stress measurements in elastic homogeneous thin shells of arbitrary shape. The stress distribution is proven to be independent of the material properties for incompressible solids, while in compressible materials it depends only on the Poisson’s ratio, which is shown to have a negligible influence on the stress state. Hence, the proposed technique enables the direct assessment of the stress field in statically indeterminate thin shells without a known material model. The shell formulation is implemented using the finite difference method to independently measure the stresses during finite inflation of planar elliptical membranes and from the deformed shapes obtained through digital image correlation during bulge tests on a hyperelastic material, showing very good agreement with finite-element predictions and the applicability of the method to nonlinear elastic materials. Therefore, the procedure can be coupled with imaging techniques for the direct assessment of stresses in thin shell structures and in the identification of material parameters through non-axisymmetric bulge tests.

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mCRE-based parameter identification from full-field measurements: Consistent framework, integrated version, and extension to nonlinear material behaviors

Cited by 13 publications

References 60 publications

NN‐mCRE: A modified constitutive relation error framework for unsupervised learning of nonlinear state laws with physics‐augmented neural networks

NN‐mCRE: A modified constitutive relation error framework for unsupervised learning of nonlinear state laws with physics‐augmented neural networks

Merging experimental design and structural identification around the concept of modified Constitutive Relation Error in low-frequency dynamics for enhanced structural monitoring

Direct stress computations in arbitrarily shaped thin shells and elliptic bulge tests

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